Premier Peter Gutwein has given a clear message to people looking to visit Tasmania: don't.
"Don't come to Tasmania," Mr Gutwein said. "We are an island that is build on tourism and visitation so it hurts me to say that.
"If you do come, you will go into self-isolation for two weeks. It's that simple."
"From 11.59 pm on Sunday March 29, hotels and other accommodation including caravan parks will be closed except for use by essential travellers, workers or permanent residents."
"We don't want non-essential presence in Tasmania," Mr Gutwein said. "I'm sorry to say it but go home."
Mr Gutwein implored Tasmanians to do what they could to work with the government on practicing social distancing and adhering to isolation rules.
"I will go to [a hard lockdown] if the advice is that we should but I want Tasmanians to know it's not two weeks, it's not four weeks - it could be six months," he said. "If we get to that point it will wreck economic havoc on this state.
"Tasmanians, please, please, do the right as we move forward.
"If you don't need to go out, don't go out. If you don't need to go to work or you don't need to go to get supplies - stay home."
When asked if Tasmania should follow the lead of New Zealand and go into a hard lockdown now for four weeks, Mr Gutwein said he did not think it was likely New Zealand's lockdown would only last a month.
There hasn't been any flagrant flaunting of self-isolation rules but the Premier said anyone doing the wrong thing would be subject to penalties.
There are now 42 confirmed cases of coronavirus in Tasmania.
Health Minister Sarah Courtney said of the six new cases diagnosed on Tuesday, three of these cases were in the North, two in the South and one in the North-West.
Ms Courtney said there was still no evidence of community transmission in Tasmania.
"All the cases were either directly or indirectly related with overseas travel," Ms Courtney said.
She said, while there may be no evidence of community transmission, this did not mean Tasmanians should relax on the rules.
Public Health director Mark Veitch said there were 240 Tasmanians from various cruise ships impacted by COVID-19 who were being monitored in isolation.
"There's another 80 people who are close contacts of cases or airplane cases who we have under active monitoring in self-isolation," Dr Veitch said.
"There's also monitoring of several thousand people who have come through the border [since the new border measures started]."